Symplectomorphisms and discrete braid invariants

Aleksander Czechowski, Robert Vandervorst*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D2, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et al. (Invent. Math. 152:369–432, 2003) and Ghrist et al. (C. R. Acad. Sci. Paris Sér. I Math. 331:861–865, 2000) to obtain a Morse type forcing theory of periodic points: a priori information about periodic points determines a mapping class which may force additional periodic points.

Original languageEnglish
Pages (from-to)231-262
Number of pages32
JournalJournal of Fixed Point Theory and Applications
Volume19
Issue number1
DOIs
Publication statusPublished - 1 Mar 2017
Externally publishedYes

Keywords

  • braids
  • Conley index
  • mapping classes
  • parabolic recurrence relations
  • Twist diffeomorphism

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